A168378 a(n) = 3 + 8*floor(n/2).

3, 11, 11, 19, 19, 27, 27, 35, 35, 43, 43, 51, 51, 59, 59, 67, 67, 75, 75, 83, 83, 91, 91, 99, 99, 107, 107, 115, 115, 123, 123, 131, 131, 139, 139, 147, 147, 155, 155, 163, 163, 171, 171, 179, 179, 187, 187, 195, 195, 203, 203, 211, 211, 219, 219, 227, 227, 235, 235

Offset

1,1

Comments

More generally, the sequences generated by the recursive relation b(n) = h*n - b(n-1) + k, with b(1)=c and h, k, c, prefixed integers, have the closed form b(n) = (2*h*n + (3*h + 2*k - 4*c)*(-1)^n + h + 2*k)/4. Also, if 2*c = h+k, then b(n) = c + h*floor(n/2); if 2*c = 2*h+k, then b(n) = c + h*floor((n-1)/2); if 2*c = k, b(n) = c + h*floor((n+1)/2). - Bruno Berselli, Sep 18 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 8*n - a(n-1) - 2, with n>1, a(1)=3.

G.f.: x*(3 + 8*x - 3*x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013

a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 18 2013

a(n) = 4*n + 2*(-1)^n + 1. - Bruno Berselli, Sep 18 2013

a(n) = A168381(n) + 1 = A168398(n) - 1. - Bruno Berselli, Sep 18 2013

E.g.f.: (4*x + 3)*cosh(x) + (4*x - 1)*sinh(x) - 3. - G. C. Greubel, Jul 19 2016

Mathematica

Table[ 3 + 8*floor(n/2), {n, 60}] (* Bruno Berselli, Sep 18 2013 *)
CoefficientList[Series[(3 + 8 x - 3 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)
LinearRecurrence[{1, 1, -1}, {3, 11, 11}, 80] (* Harvey P. Dale, Oct 05 2022 *)

Prog

(Magma) [3+8*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

Crossrefs

Cf. A017101, A168381, A168398.

Sequence in context: A303122 A080351 A178709 * A248410 A059200 A232038

Adjacent sequences: A168375 A168376 A168377 * A168379 A168380 A168381

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 24 2009

Extensions

New definition by Vincenzo Librandi, Sep 18 2013

Status

approved